{"date_created":"2018-12-11T11:52:11Z","status":"public","publication_status":"published","publisher":"Springer","date_updated":"2021-01-12T06:50:56Z","_id":"1465","abstract":[{"text":"We prove a generating function formula for the Betti numbers of Nakajima quiver varieties. We prove that it is a q-deformation of the Weyl-Kac character formula. In particular this implies that the constant term of the polynomial counting the number of absolutely indecomposable representations of a quiver equals the multiplicity of a certain weight in the corresponding Kac-Moody algebra, which was conjectured by Kac in 1982.","lang":"eng"}],"page":"21 - 37","acknowledgement":"This work has been supported by a Royal Society University Research Fellowship, NSF grants DMS-0305505 and DMS-0604775 and an Alfred Sloan Fellowship 2005-2007.","main_file_link":[{"url":"http://arxiv.org/abs/0811.1569","open_access":"1"}],"intvolume":" 181","extern":1,"publication":"Inventiones Mathematicae","title":"Kac's conjecture from Nakajima quiver varieties","citation":{"mla":"Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” Inventiones Mathematicae, vol. 181, no. 1, Springer, 2010, pp. 21–37, doi:10.1007/s00222-010-0241-3.","short":"T. Hausel, Inventiones Mathematicae 181 (2010) 21–37.","ista":"Hausel T. 2010. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 181(1), 21–37.","ama":"Hausel T. Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. 2010;181(1):21-37. doi:10.1007/s00222-010-0241-3","apa":"Hausel, T. (2010). Kac’s conjecture from Nakajima quiver varieties. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-010-0241-3","ieee":"T. Hausel, “Kac’s conjecture from Nakajima quiver varieties,” Inventiones Mathematicae, vol. 181, no. 1. Springer, pp. 21–37, 2010.","chicago":"Hausel, Tamás. “Kac’s Conjecture from Nakajima Quiver Varieties.” Inventiones Mathematicae. Springer, 2010. https://doi.org/10.1007/s00222-010-0241-3."},"year":"2010","date_published":"2010-07-01T00:00:00Z","issue":"1","day":"01","author":[{"first_name":"Tamas","full_name":"Tamas Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","last_name":"Hausel"}],"quality_controlled":0,"month":"07","publist_id":"5730","volume":181,"oa":1,"type":"journal_article","doi":"10.1007/s00222-010-0241-3"}